Compressible Flow in a Nozzle.docx
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Compressible Flow in a Nozzle.docx
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CompressibleFlowinaNozzle
CompressibleFlowinaNozzle
ProblemSpecification
Considerairflowingathigh-speedthroughaconvergent-divergentnozzlehavingacircularcross-sectionalarea,A,thatvarieswithaxialdistancefromthethroat,x,accordingtotheformula
A=0.1+x2;-0.5 whereAisinsquaremetersandxisinmeters.Thestagnationpressurepoattheinletis101,325Pa.ThestagnationtemperatureToattheinletis300K.Thestaticpressurepattheexitis3,738.9Pa.WewillcalculatetheMachnumber,pressureandtemperaturedistributioninthenozzleusingFLUENTandcomparethesolutiontoquasi-1Dnozzleflowresults.TheReynoldsnumberforthishigh-speedflowislarge.Soweexpectviscouseffectstobeconfinedtoasmallregionclosetothewall.Soitisreasonabletomodeltheflowasinviscid. Step1: CreateGeometryinGAMBIT Sincethenozzlehasacircularcross-section,it'sreasonabletoassumethattheflowisaxisymmetric.Sothegeometrytobecreatedistwo-dimensional. StartGAMBIT Createanewfoldercallednozzleandselectthisastheworkingdirectory.Add-idnozzletothestartupoptions. CreateAxisEdge We'llcreatethebottomedgecorrespondingtothenozzleaxisbycreatingverticesAandBshownintheproblemspecificationandjoiningthembyastraightline. OperationToolpad>GeometryCommandButton >VertexCommandButton >CreateVertex Createthefollowingtwovertices: Vertex1: (-0.5,0,0) Vertex2: (0.5,0,0) OperationToolpad>GeometryCommandButton >EdgeCommandButton >CreateEdge Selectvertex1byholdingdowntheShiftbuttonandclickingonit.Next,selectvertex2.ClickApplyintheCreateStraightEdgewindow. CreateWallEdge We'llnextcreatethebottomedgecorrespondingtothenozzlewall.Thisedgeiscurved.Since A=pir2 wherer(x)istheradiusofthecross-sectionatxand A=0.1+x2 forthegivennozzlegeometry,weget r(x)=[(0.1+x2)/pi]0.5;-0.5 Thisistheequationofthecurvedwall.LifewouldhavebeeneasierifGAMBITallowedforthisequationtobeentereddirectlytocreatethecurvededge.Instead,onehastocreateafilecontainingthecoordinatesofaseriesofpointsalongthecurvedlineandreadinthefile.Themorenumberofpointsusedalongthecurvededge,thesmoothertheresultantedge. Thefilevert.datcontainsthepointdefinitionsforthenozzlewall.Takealookatthisfile.Thefirstlineis 211 whichsaysthatthereare21pointsalongtheedgeandwearedefiningonly1edge.Thisisfollowedbyx,randzcoordinatesforeachpointalongtheedge.Ther-valueforeachxwasgeneratedfromtheaboveequationforr(x).Thez-coordinateis0forallpointssincewehavea2Dgeometry. Right-clickonvert.datandselectSaveAs...todownloadthefiletoyourworkingdirectory. MainMenu>File>Import>ICEMInput... NexttoFileName: enterthepathtothevert.datfilethatyoudownloadedorbrowsetoitbyclickingontheBrowsebutton. Then,checktheVerticesandEdgesboxesunderGeometrytoCreateaswewanttocreatetheverticesaswellasthecurvededge. ClickAccept. Thisshouldcreatethecurvededge.Hereitisinrelationtotheverticeswecreatedabove: CreateInletandOutletEdges Createtheverticaledgefortheinlet: OperationToolpad>GeometryCommandButton >EdgeCommandButton >CreateEdge Shift-clickonvertex1andthenthevertexaboveittocreatetheinletedge. Similarly,createtheverticaledgefortheoutlet. CreateFace Formafaceoutoftheareaenclosedbythefouredges: OperationToolpad>GeometryCommandButton >FaceCommandButton >FormFace Recallthatwehavetoshift-clickoneachoftheedgesenclosingthefaceandthenclickApplytocreatetheface. SaveYourWork MainMenu>File>Save Thiswillcreatethenozzle.dbsfileinyourworkingdirectory.Checkthatithasbeencreatedsothatyouwillabletoresumefromhereifnecessary. Step2: MeshGeometryinGAMBIT Nowthatwehavethebasicgeometryofthenozzlecreated,weneedtomeshit.Wewouldliketocreatea50x20gridforthisgeometry. MeshEdges Asintheprevioustutorials,wewillfirststartbymeshingtheedges. OperationToolpad>MeshCommandButton >EdgeCommandButton >MeshEdges LiketheLaminarPipeFlowTutorial,wearegoingtouseevenspacingbetweeneachofthemeshpoints.Wewon'tbeusingtheGradingthistime,sodeselecttheboxnexttoGradingthatsaysApply. Then,changeIntervalCountto20forthesideedgesandIntervalCountto50forthetopandbottomedges. MeshFace Nowthatwehavetheedgesmeshed,weneedtomeshtheface. OperationToolpad>MeshCommandButton >FaceCommandButton >MeshFaces Asbefore,selectthefaceandclicktheApplybutton. SaveYourWork MainMenu>File>Save Step3: SpecifyBoundaryTypesinGAMBIT SpecifyBoundaryTypes Nowthatwehavethemesh,wewouldliketospecifytheboundaryconditionshereinGAMBIT. OperationToolpad>ZonesCommandButton >SpecifyBoundaryTypesCommandButton ThiswillbringuptheSpecifyBoundaryTypeswindowontheOperationPanel.Wewillfirstspecifythattheleftedgeistheinlet.UnderEntity: pickEdgessothatGAMBITknowswewanttopickanedge(faceisdefault). NowselecttheleftedgebyShift-clickingonit.TheselectededgeshouldappearintheyellowboxnexttotheEdgesboxyoujustworkedwithaswellastheLabel/TypelistrightundertheEdgesbox. NexttoName: enterinlet. ForType: selectWALL. ClickApply.YoushouldseethenewentryappearunderName/Typeboxnearthetopofthewindow. Repeatfortheoutlet,centerline,andwalledges. YoushouldhavethefollowingedgesintheName/Typelistwhenfinished: SaveandExport MainMenu>File>Save MainMenu>File>Export>Mesh... Typeinnozzle.mshfortheFileName: .SelectExport2dMeshsincethisisa2dimensionalmesh.ClickAccept. Checknozzle.mshhasbeencreatedinyourworkingdirectory. Step4: SetUpProbleminFLUENT Ifyouhaveskippedthepreviousmeshgenerationsteps1-3,youcandownloadthemeshbyright-clickingonthislink.Savethefileasnozzle.mshinyourworkingdirectory.Youcanthenproceedwiththeflowsolutionstepsbelow. LaunchFLUENT Start>Programs>FluentInc>FLUENT6.3.26>FLUENT6.3.26 Select2ddpfromthelistofoptionsandclickRun. ImportFile MainMenu>File>Read>Case... Navigatetoyourworkingdirectoryandselectthenozzle.mshfile.ClickOK. ThefollowingshouldappearintheFLUENTwindow: Checkthatthedisplayedinformationisconsistentwithourexpectationsofthenozzlegrid. CheckandDisplayGrid First,wecheckthegridtomakesurethattherearenoerrors. MainMenu>Grid>Check Anyerrorsinthegridwouldbereportedatthistime.Checktheoutputandmakesurethattherearenoerrorsreported. Grid>Info>Size Howmanycellsandnodesdoesthegridhave? MainMenu>Display>Grid MakesureallitemsunderSurfacesisselected.ThenclickDisplay.Thegraphicswindowopensandthegridisdisplayedinit. Someoftheoperationsavailableinthegraphicswindoware: Translation: ThegridcanbetranslatedinanydirectionbyholdingdowntheLeftMouseButtonandthenmovingthemouseinthedesireddirection. ZoomIn: HolddowntheMiddleMouseButtonanddragaboxfromtheUpperLeftHandCornertotheLowerRightHandCornerovertheareayouwanttozoominon. ZoomOut: HolddowntheMiddleMouseButtonanddragaboxanywherefromtheLowerRightHandCornertotheUpperLeftHandCorner. Thegridhas50divisionsintheaxialdirectionand20divisionsintheradialdirection.Thetotalnumberofcellsis50x20=1000.Sinceweareassuminginviscidflow,wewon'tberesolvingtheviscousboundarylayeradjacenttothewall.(Theeffectoftheboundarylayerissmallinourcaseandcanbeneglected.)Thus,wedon'tneedtoclusternodestowardsthewall.Sothegridhasuniformspacingintheradialdirection.Wealsouseuniformspacingintheaxialdirection. Lookatspecificpartsofthegridbychoosingeachboundary(centerline,inlet,etc)listedunderSurfacesintheGridDisplaymenu.Clicktoselectandclickagaintodeselectaspecificboundary.ClickDisplayafteryouhaveselectedyourboundaries. DefineSolverProperties Define>Models>Solver... WeseethatFLUENTofferstwomethods("solvers")forsolvingthegoverningequations: Pressure-BasedandDensity-Based.Tofigureoutthebasicdifferencebetweenthesetwosolvers,let'sturntothedocumentation. MainMenu>Help>User'sGuideContents... ThisshouldbringupFLUENT6.3User'sGuideinyourwebbrowser.Ifnot,accesstheUser'sGuidefromtheStartmenu: Start>Programs>FluentIncProducts>Fluent6.3Documentation>Fluent6.3Documentation.ThiswillbringuptheFLUENTdocumentationinyourbrowser.Clickonthelinktotheuser'sguide. Gotochapter25intheuser'sguide;itdiscussesthePressure-BasedandDensity-Basedsolvers.Section25.1introducesthetwosolvers: "Historicallyspeaking,thepressure-basedapproachwasdevelopedforlow-speedincompressibleflows,whilethedensity-basedapproachwasmainlyusedforhigh-speedcompressibleflows.However,recentlybothmethodshavebeenextendedandreformulatedtosolveandoperateforawiderangeofflowconditionsbeyondtheirtraditionalororiginalintent." "Inbothmethodsthevelocityfieldisobtainedfromthemomentumequations.Inthedensity-basedapproach,thecontinuityequationisusedtoobtainthedensityfieldwhilethepressurefieldisdeterminedfromtheequationofstate." "Ontheotherhand,inthepressur
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